The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1
 0  X  0  0  0  0  X  X  X aX  0  X (a+1)X aX (a+1)X aX  X  X aX  0 (a+1)X  X (a+1)X  0  X (a+1)X aX aX  X  0  X (a+1)X (a+1)X (a+1)X aX (a+1)X (a+1)X  X  0 (a+1)X  X aX  0  0  X  0  X
 0  0  X  0  0  X (a+1)X aX aX aX  0  0 aX aX  0 aX (a+1)X aX (a+1)X (a+1)X aX  0  0 (a+1)X (a+1)X (a+1)X  X (a+1)X  0 (a+1)X  0 (a+1)X  0 (a+1)X  X (a+1)X aX aX aX  0 aX (a+1)X  0  0 aX aX (a+1)X
 0  0  0  X  0 (a+1)X  0  X aX (a+1)X  X  X  X  0  X (a+1)X  X  X (a+1)X (a+1)X (a+1)X  0 (a+1)X (a+1)X  0  0 aX  0 aX aX  0  X (a+1)X (a+1)X  0 aX aX (a+1)X aX  0 (a+1)X  0  X  X  X (a+1)X (a+1)X
 0  0  0  0  X  X  X (a+1)X  X  X  X aX  0  0  0 aX  X aX (a+1)X (a+1)X  0  X aX aX aX aX  0  X  X  0 aX  X  0 aX  X  X aX  X  0  0 (a+1)X aX  X aX  X (a+1)X  X

generates a code of length 47 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+144x^128+174x^132+192x^135+177x^136+1152x^139+150x^140+1728x^143+90x^144+69x^148+72x^152+48x^156+33x^160+30x^164+27x^168+6x^172+3x^180

The gray image is a linear code over GF(4) with n=188, k=6 and d=128.
This code was found by Heurico 1.16 in 0.141 seconds.